PCA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be53dd9c",
   "metadata": {},
   "source": [
    "# Random Gaussian distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fa0b9a4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import necessary libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bc3d45ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Generate a normal(Gaussian) distribution\n",
    "np.random.seed(0)\n",
    "mat1 = np.random.randn(20,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f1fe1f22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the generated matrix\n",
    "plt.scatter(mat1[:,0], mat1[:,1], marker='d')\n",
    "plt.suptitle(\"Original Data\", fontsize=12, fontweight='bold')\n",
    "plt.title(\"(THA076BEI005 & THA076BEI025)\", fontsize=10)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2c4cfe31",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Generate uniform distribution matrix between[0,1]\n",
    "mat2 = np.random.uniform(0, 1, (2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f4d6a171",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Matrix multiplication\n",
    "mat_product = np.dot(mat1,mat2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "61aecb89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the product matrix\n",
    "plt.scatter(mat_product[:,0],mat_product[:,1], marker='d')\n",
    "plt.suptitle(\"Transformed Data\", fontsize=12, fontweight='bold')\n",
    "plt.title(\"(THA076BEI005 & THA076BEI025)\", fontsize=10)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d431672e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance along x-axis:  0.4375836468357111\n",
      "Variance along x-axis:  0.3433699581975217\n"
     ]
    }
   ],
   "source": [
    "#Calculate variance against both axis\n",
    "var_x = np.var(mat_product[:,0])\n",
    "var_y = np.var(mat_product[:,1])\n",
    "print(\"Variance along x-axis: \", var_x)\n",
    "print(\"Variance along x-axis: \", var_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f36ac543",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance Matrix\n",
      " [[0.51259458 0.45525796]\n",
      " [0.45525796 0.419432  ]]\n"
     ]
    }
   ],
   "source": [
    "#Calculate the Covariance matrix\n",
    "Sx = (1/(len(mat_product)-1))*np.dot(mat_product.T,mat_product)\n",
    "print(\"Covariance Matrix\\n\",Sx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "98341dac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigen values\n",
      " [0.92364811 0.00837847]\n",
      "\n",
      "Eigen vector\n",
      " [[ 0.74222201 -0.67015407]\n",
      " [ 0.67015407  0.74222201]]\n"
     ]
    }
   ],
   "source": [
    "#Calculate eigenvalues & eigenvectors\n",
    "eigenvalues, eigenvector = np.linalg.eig(Sx)\n",
    "print(\"Eigen values\\n\",eigenvalues)\n",
    "print(\"\\nEigen vector\\n\",eigenvector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "34d63ced",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance proportion:  [99.10104829  0.89895171]\n"
     ]
    }
   ],
   "source": [
    "#Variance of eigenvalues\n",
    "total_var = np.sum(eigenvalues)\n",
    "var_prop = (eigenvalues / total_var) * 100\n",
    "print(\"Variance proportion: \",var_prop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "26df2f89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 20)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Compute output\n",
    "y = np.dot(eigenvector.T,mat_product.T)\n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bc13f86e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covaraince matrix\n",
      " [[ 1.75493141e+01 -1.72718104e-15]\n",
      " [-1.72718104e-15  1.59190909e-01]]\n"
     ]
    }
   ],
   "source": [
    "#Covaraince matrix of output\n",
    "Sy = (1/(len(y)-1))*np.dot(y,y.T)\n",
    "print(\"Covaraince matrix\\n\",Sy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "02e4b132",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jtWnTJmVlZbkc66ZNm6pu3br5HutZs2YpJCRE99xzj3Ns8eLF6tChg1599VXVrl1bjRs31lNPPaVz587lW1tGRoZmzJihsLCwXDNH7khMTFTLli1Vq1Yt51hsbKzS09PzPVY5OTk6deqUqlWr5jK+Z88eRUZGqmHDhho4cKAOHjyYa9uOHTu6fL8ARUEQAoro559/VmRkZLG2Xbp0qSpVquRy69GjR671Pv74Y91www1q0aKF/P39dd999+n99993Lr90ztDlv1gu3c/rfCJJev/99xUbG6vrrrvOOfbTTz/p559/1rx58zRr1izFxcVp06ZNLr9AJSktLc1Zb2BgoB599FG99957uv76613We+edd3L199FHH+VZz9GjR11etpGkChUqqFq1as4ejh49mmePlz8HTZo00fTp07Vo0SJ9+OGHysnJUefOnXXo0KE8H1eSfvjhBw0YMEATJkzQQw89pHnz5jmXbdq0SQ6HQ7/99lu+2xdFXs/F5edLXTJ9+nT16NFDVatWVbVq1RQbG6sZM2Y4lx89elSBgYG5zi0q7FgPGDBAFStWdI799NNPWrt2rbZv364FCxbojTfe0Keffqq//e1vLttu27bNWW/FihU1adIkzZkzR6GhoS7rPfvss7n6yy98FOU4XmnSpEk6ffq0+vbt6xzr1KmT4uLitGzZMr377rvav3+/brnlFp06dcpl28jIyCK9PApcroKnCwB8xblz54p0Mm5ebrvtNr377rsuY+vXr9f999/vMjZ9+nSXsfvvv19dunTRf/7zH1WuXNntxz106JCWL1+uTz75xGU8JydHGRkZmjVrlho3bizp4i/R9u3ba/fu3c5ZgMqVK2vz5s2SLp4jtXLlSj3yyCO69tpr1atXL+f+Bg4cqH/84x8uj3HlL8CSFhUVpaioKOf9zp07q1mzZpo6daomTpyY5zbjxo1Tjx49NGrUKMXExKhbt246fvy4HnnkEW3btk1NmzZV9erVr6quvJ6L+fPn66WXXnLevzS79uabbzrH7r//fj311FMaM2aM/Pzc/xs1MTFRO3fu1AcffOAynpOTI4fDoY8++khVqlSRJL3++uu655579M477zhDU5MmTbR48WJJF2cm586dq3vvvVdfffWVy+zd008/rSFDhrg8Ru3atd2uNy+zZ8/W+PHjtWjRIpewfPkfDa1atVKnTp1Ur149ffLJJ85z9iSpYsWKOnv2bInUAnsQhIAiql69usvLMu645ppr1KhRI5exK2cufvjhB3377bfasGGDy9Uv2dnZ+vjjjzVs2DCFh4dLklJSUhQREeFcJyUlRW3atMn1uDNmzNC1116rO++802U8IiJCFSpUcIYgSWrWrJmki1f5XApCfn5+LnW3atVKK1as0CuvvOIShKpUqZKrv/yEh4e7XNEkSRcuXNCJEyec/YWHh7tcHXWpx0vL8hIQEKC2bdtq7969+T721q1bNXjwYEkXX95bvHixYmNj9dtvv2nZsmUuLx8WV17PxZUzYMuXL9fhw4fVr18/l/Hs7GytWrVK3bp1U3h4uDIzM5WamuoyK5SSkpLnczBt2jS1adMm18u3ERERql27tjMESRePtTFGhw4d0g033CDp4pVXl9fdtm1bLVy4UG+88YY+/PBD53j16tXdOtYbNmxwGcvvOH788cfOWbrLXw7MS1hYmBo3bpzrWJ84cUI1atQoUm3AJbw0BhRR27Zt9cMPP5Ta/t9//33deuut+v7775WUlOS8jRgxwvnyWIMGDRQeHq5Vq1Y5t0tPT9f69etdZkeki5fHz5gxQ4MGDVJAQIDLsptuukkXLlzQvn37nGM//vijJKlevXoF1unv71/g+SWFiYqKUmpqqjZt2uQc+/LLL5WTk6NOnTo511mzZo2ysrKc68THx6tJkyaqWrVqnvvNzs7Wtm3bXALilWrXru3yMs5NN92kBQsWaOLEidq3b58ef/zxYvfljvfff1/33Xefy3FOSkpyeSm0ffv2CggIcDnWu3fv1sGDB3Md69OnT+eaHbnkpptu0pEjR1zenuDHH3+Un5+fy8uleSmJY71t2zaX4BsfH6/Q0FA1b97cOTZnzhwNHTpUc+bMUc+ePQvd7+nTp7Vv375cx3r79u1q27ZtseuFpTx9tjbgK7Zu3WoqVKhgTpw4kefyq7lq7NKVXe+++26u9S5dZbV9+3ZjjDEvv/yyCQsLM4sWLTJbt241vXv3Ng0aNDDnzp1z2W7lypVGktm5c2eufWZnZ5t27dqZW2+91WzevNls3LjRdOrUyeXKpRkzZpjQ0FCTnJxskpOTzU8//WSmTp1q/P39Xa7o6dKlixk2bJhzvUu3y58nXXGVVffu3U3btm3N+vXrzdq1a80NN9zgciVXamqqqVWrlnnggQfM9u3bzccff2xCQkLM1KlTneuMHz/eLF++3Ozbt89s2rTJ3HfffSY4ONjs2LEjV7+XXLo67W9/+5vZtm2b2bx5s/nHP/5hKlWqZPz9/c3HH3+c77aXu7Kfy5+Lwq4au3Rl1xdffJFrvc8//9wEBQU5r/B65JFHTN26dc2XX35pNm7caKKiokxUVFSu7aZNm2aCg4NzXYFojDGnTp0y1113nbnnnnvMjh07zOrVq80NN9xgHnroIec6Y8eONS1atHAeux9//NFMnDjRSDIzZ850rlevXj0zYcKEXMc6LS3NGJP7qrELFy6YG2+80cTExJikpCSzbNkyU6NGDTN69GjnPj/66CNToUIF8/bbb7vsMzU11bnOyJEjTUJCgtm/f7/55ptvTHR0tKlevbo5duyYS6/16tVzuWIOKAqCEOCGjh07milTpuS57GqC0KeffprrMuPLNWvWzDz55JPGmIuX0D///POmVq1aJigoyNx+++1m9+7dubbp37+/6dy5c769HD582Pz5z382lSpVMrVq1TJDhgxxucR6xowZRpLzFhQUZBo3bmxefPFFc+HCBed6Xbp0cVnv0i02Nta5zpXB4fjx46Z///6mUqVKJjQ01AwdOtScOnXKpb7vv//e3HzzzSYoKMjUrl3bvPzyyy7Lhw8fburWrWsCAwNNrVq1zB133GE2b96cb7+XfPnll+aWW24xoaGhJiwszNxzzz3mhx9+MC+88IIJDg4233zzTaH7uJogNGnSJBMWFmYyMzNzrZeRkWHCwsLMm2++aYwx5ty5c+Zvf/ubqVq1qgkJCTF33XWXSU5OzrVdVFSUGTBgQL717ty500RHR5uKFSua6667zowYMcKcPXvWuXzs2LEuxy4kJMS0bNkyVzCvV69ensf6r3/9qzEmdxAyxpgDBw6YHj16mIoVK5rq1aubkSNHmqysLJfnLK99Dh482LlOv379TEREhAkMDDS1a9c2/fr1M3v37nWpbd26dSYsLMylL6AoHMYYU/rzTkD58Nlnn+npp5/W9u3bi3VCK4DS0a9fP7Vu3VrPPfecp0uBj+FkacANPXv21J49e3T48GHVqVPH0+UA0MXPGmvZsqWefPJJT5cCH8SMEAAAsBZz+wAAwFoEIQAAYC2CEAAAsBYnSxciJydHR44cUeXKleVwODxdDgAAKAJjjE6dOqXIyMgCr/IlCBXiyJEjXB0EAICP+uWXXwp8F3WCUCEufdDlL7/84vwU5qysLK1YsUIxMTG5PrqgvLChR8mOPm3oUbKjTxt6lOzo04YeJc/2mZ6erjp16hT6gdUEoUJcejksNDTUJQiFhIQoNDS03P4HtqFHyY4+behRsqNPG3qU7OjThh4l7+izsNNaOFkaAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtnwpCa9asUa9evRQZGSmHw6GFCxcWuH5CQoIcDkeu29GjR8umYAAA4NV8KgidOXNGrVu31ttvv+3Wdrt371ZycrLzVrNmzVKqEAAA+BKfemfpHj16qEePHm5vV7NmTYWFhZV8QQAAwKf5VBAqrjZt2igjI0M33nijxo0bp5tuuinfdTMyMpSRkeG8n56eLuni24RnZWU5v7783/LIhh4lO/q0oUfJjj5t6FGyo08bepQ822dRH9NhjDGlXEupcDgcWrBggfr06ZPvOrt371ZCQoI6dOigjIwMTZs2TR988IHWr1+vdu3a5bnNuHHjNH78+Fzjs2fPVkhISEmVDwAAStHZs2c1YMAApaWlOT8rNC/lOgjlpUuXLqpbt64++OCDPJfnNSNUp04d/fbbby4fuhofH69u3bqV2w/Ls6FHyY4+behRsqNPG3qU7OjThh4lz/aZnp6u6tWrFxqErHhp7HIdO3bU2rVr810eFBSkoKCgXOMBAQG5DmJeY+WNDT1KdvRpQ4+SHX3a0KNkR5829Ch5ps+iPp5PXTVWEpKSkhQREeHpMgAAgBfwqRmh06dPa+/evc77+/fvV1JSkqpVq6a6detq9OjROnz4sGbNmiVJeuONN9SgQQO1aNFC58+f17Rp0/Tll19qxYoVnmoBAAB4EZ8KQhs3btRtt93mvD9ixAhJ0uDBgxUXF6fk5GQdPHjQuTwzM1MjR47U4cOHFRISolatWmnlypUu+wAAAPbyqSDUtWtXFXRud1xcnMv9Z555Rs8880wpVwUAAHyVdecIAQAAXEIQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsJZPBaE1a9aoV69eioyMlMPh0MKFCwvdJiEhQe3atVNQUJAaNWqkuLi4Uq8TAAD4Bp8KQmfOnFHr1q319ttvF2n9/fv3q2fPnrrtttuUlJSk4cOH66GHHtLy5ctLuVIAAOALKni6AHf06NFDPXr0KPL6U6ZMUYMGDfTvf/9bktSsWTOtXbtWkydPVmxsbGmVCQAAfIRPBSF3JSYmKjo62mUsNjZWw4cPz3ebjIwMZWRkOO+np6dLkrKyspSVleX8+vJ/yyMbepTs6NOGHiU7+rShR8mOPm3oUfJsn0V9zHIdhI4ePapatWq5jNWqVUvp6ek6d+6cKlasmGubf/3rXxo/fnyu8RUrVigkJMRlLD4+vmQL9kI29CjZ0acNPUp29GlDj5IdfdrQo+SZPs+ePVuk9cp1ECqO0aNHa8SIEc776enpqlOnjmJiYhQaGirpYsqMj49Xt27dFBAQ4KlSS5UNPUp29GlDj5IdfdrQo2RHnzb0KHm2z0uv6BSmXAeh8PBwpaSkuIylpKQoNDQ0z9kgSQoKClJQUFCu8YCAgFwHMa+x8saGHiU7+rShR8mOPm3oUbKjTxt6lDzTZ1Efz6euGnNXVFSUVq1a5TIWHx+vqKgoD1UEAAC8iU8FodOnTyspKUlJSUmSLl4en5SUpIMHD0q6+LLWoEGDnOs/8sgj+umnn/TMM89o165deuedd/TJJ5/oySef9ET5AADAy/hUENq4caPatm2rtm3bSpJGjBihtm3basyYMZKk5ORkZyiSpAYNGuizzz5TfHy8WrdurX//+9+aNm0al84DAABJPnaOUNeuXWWMyXd5Xu8a3bVrV23ZsqUUqwIAAL7Kp2aEAAAAShJBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLV8Lgi9/fbbql+/voKDg9WpUydt2LAh33Xj4uLkcDhcbsHBwWVYLQAA8GY+FYTmzp2rESNGaOzYsdq8ebNat26t2NhYHTt2LN9tQkNDlZyc7Lz9/PPPZVgxAADwZj4VhF5//XUNGzZMQ4cOVfPmzTVlyhSFhIRo+vTp+W7jcDgUHh7uvNWqVasMKwYAAN6sgqcLKKrMzExt2rRJo0ePdo75+fkpOjpaiYmJ+W53+vRp1atXTzk5OWrXrp1eeukltWjRIt/1MzIylJGR4byfnp4uScrKylJWVpbz68v/LY9s6FGyo08bepTs6NOGHiU7+rShR8mzfRb1MR3GGFPKtZSII0eOqHbt2lq3bp2ioqKc488884xWr16t9evX59omMTFRe/bsUatWrZSWlqZJkyZpzZo12rFjh6677ro8H2fcuHEaP358rvHZs2crJCSk5BoCAACl5uzZsxowYIDS0tIUGhqa73o+MyNUHFFRUS6hqXPnzmrWrJmmTp2qiRMn5rnN6NGjNWLECOf99PR01alTRzExMc4nMisrS/Hx8erWrZsCAgJKtwkPsaFHyY4+behRsqNPG3qU7OjThh4lz/Z56RWdwvhMEKpevbr8/f2VkpLiMp6SkqLw8PAi7SMgIEBt27bV3r17810nKChIQUFBeW575UHMa6y8saFHyY4+behRsqNPG3qU7OjThh4lz/RZ1MfzmZOlAwMD1b59e61atco5lpOTo1WrVrnM+hQkOztb27ZtU0RERGmVCQAAfIjPzAhJ0ogRIzR48GB16NBBHTt21BtvvKEzZ85o6NChkqRBgwapdu3a+te//iVJmjBhgv7whz+oUaNGSk1N1Wuvvaaff/5ZDz30kCfbAAAAXsKnglC/fv3066+/asyYMTp69KjatGmjZcuWOS+JP3jwoPz8fp/kOnnypIYNG6ajR4+qatWqat++vdatW6fmzZt7qgUAAOBFfCoISdLjjz+uxx9/PM9lCQkJLvcnT56syZMnl0FVAADAF/nMOUIAAAAljSAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIASi3LmTneLoEAF6OIASgXPr2p+NqOzFe63867ulSAHgxghCAcicrO0ej52/TqfMXNHrBNmUxMwQgHwQhAOXOzHUHtP+3M5Kkn349o5nrDni2IABeiyAEoFw5dipDk1bsdhn794oflZJ+3kMVAfBmBCEA5cpry3YpK9u4jGVm5+jFz3Z6qCIA3owgBKBc+WLHUWXnuAah7Byjxd8fUeK+4p04zdVnQPlFEAJQrvg58h//7+ZDbu+Pq8+A8o0gBKBcuWIyyGX8nvbXubUvrj4Dyj+CEIBypUeLcPlfMS3k7+fQna0j9YeG17q1L64+A8o/ghCAcuXp7k0V4O8ahAL9/fSPns3c2k9K+nmuPgMsQBACUK7UrBykp2KauIyNjGmsWqHBbu3nhaU/cPUZYAGCEIByZ3Dn+mpY4xpJUsMa12hw5/pubb9u329asjW5xK8+A+B9CEIAyp0Afz+9dFdLVQ6uoH/d1VIB/u79qJu/+XCJX31WVrjUH3APQQiA1ymJX+Z/aHittjzfTZ3cPEFaku5ud12JXn1WVrjUH3AfQQiAVynJX+YV3JwJuiTq+mvVq1VEiV19Vha41P93zIrBHQQhAF7Dm36Z//NPzUvk6rOywqX+FzErBncRhAALeetfzN70y7xWaHCJXH12SWk+51zqf5E3BWn4DoKQB3nrLyOUb976F7M3/jK/2qvPLint55xL/S/ypiAN30EQ8hBv/WWE8s2b/2L2xl/mV3v1mVT6zzmX+l/kjUEavoEg5AHe/MsI5Zu3/sXszb/Mr+bqM+nqnvOizBr78qX+JckbgzR8g9tBKDk5WR9++KE+//xzZWZmuiw7c+aMJkyYUGLFlVfe+ssI5duxUxle+xezt/8yL+7VZ1czS1HUWWNfvdS/JHlzkIb3c+u7+7vvvlPz5s312GOP6Z577lGLFi20Y8cO5/LTp09r/PjxJV5kecL0LTzltWW7vPYv5vL6y7y4sxTuzBr74qX+Jc3bgzS8m1tB6LnnntNdd92lkydPKiUlRd26dVOXLl20ZcuW0qqv3GH6Fp7yxY6jXvsXc3n8ZX41sxTuzhr72qX+Ja28BmmUDbeC0KZNmzRq1Cj5+fmpcuXKeuedd/TUU0/p9ttv13fffVdaNZYbTN/Ck7z9L+a8fpn7Oxw++8u8uLMUxZk1LulL/X2NLwRpb71K2FvrKktuv/B9/rzrN+OoUaP03HPPKSYmRuvWrSuxwsojpm/hSUX9i9lTPxjz+mVeObiCql0T6JF6rlZxZymKO2tcUpf6+ypvnhXz1quEvbWusuZWELrxxhvzDDtPPfWURo8erf79+5dYYeUR07fwpB4twgv9i9nTPxgHd67vEnyOn8n02YsJijNLUdis8Yb9J/J9vJK41N+XeeusmLdeJeytdXmCW98pgwYN0tq1a/Nc9swzz2j8+PGqW7duiRRWHvnC9C3Kr6e7Ny3wL2Zv+MF44kymTp+/4DLmyxcTuDtLUdis8eLvjxT4eFd7qb+v88ZZMW+9Sthb6/IEt4LQQw89pA8//DDf5c8++6z2799/1UUV5O2331b9+vUVHBysTp06acOGDQWuP2/ePDVt2lTBwcFq2bKlPv/881KtrzDePH2L8q1m5aAC/2L2hh+MLyz9Qdmm4JeFvOmchsJqqRUarCejG7uMDY++Id9ZisJmjXu3iSy0puJe6l8eeNusmLdeJeytdXmKW/9Lzp8/r8WLF+vUqVO5lqWnp2vx4sXKyMgoseKuNHfuXI0YMUJjx47V5s2b1bp1a8XGxurYsWN5rr9u3Tr1799fDz74oLZs2aI+ffqoT58+2r59e6nVWBhvnb6FHfL7i9kbfjAW5WICT790d7ni1uLIZ8ZHujhrHFkl758FtcOC9T/1q7n1WDbyplkxb71K2Fvr8hS3gtDUqVP15ptvqnLlyrmWhYaG6q233tL//d//lVhxV3r99dc1bNgwDR06VM2bN9eUKVMUEhKi6dOn57n+m2++qe7du+vpp59Ws2bNNHHiRLVr107/+7//W2o1FoU3Tt/CDvn9xewNPxgLe1lo3qZfPP7S3SVFfRkxJf28Jq/80WVscvyefAPmun2/6Uha3ssOp54v8Bwh/M4bZsWu5nwvT9Zl49XLFdxZ+aOPPtLzzz+f7/Lhw4drwoQJevzxx6+6sCtlZmZq06ZNGj16tHPMz89P0dHRSkxMzHObxMREjRgxwmUsNjZWCxcuzPdxMjIyXGa10tPTJUlZWVnKyspyfn35v8Xxwp3N9P/N2aIX72wm5WQrKye72PsqDSXRoy+woc8re2xfJ1QbRnVVBX8/ZWVlaf3+41qx44gqOKQK/pdvabR8+2F982OkOjYo/ZmIu1qHa0nSL/kurxzopyMnTyvIXzp84rRmfbNPg6LqO5eX5bGclXigwFou+dfS7fJTjoL8f/+l41C2Xv5sh169p1Wu9Rdt/kUVK5g8Xx7zc0iffX9InQLL9/9XqXx8X3rrsSysroWbD6pD3dASezxPHsuiPqbDGJPPK9K5Va1aVd9//32+J0QfPHhQrVu31smTJ4u6yyI7cuSIateurXXr1ikqKso5/swzz2j16tVav359rm0CAwM1c+ZMl6vZ3nnnHY0fP14pKSl5Ps64cePyfHfs2bNnKyQkpAQ6AQAApe3s2bMaMGCA0tLSFBqaf7hza0bowoUL+vXXX/MNQr/++qsuXLiQ5zJfMXr0aJdZpPT0dNWpU0cxMTHOJzIrK0vx8fHq1q2bAgICPFVqqbKhR8mOPgvrccP+E/rLzPzfEHXGkP8ps3NTjp3K0B1vrtH5C7+/1FSxgr+irq+m1Xt+c5nO9/dzKLZ5uHNmpayO5dPzvteKnSkF1iJJ/1y4XYu/P5zvX953tq6tF/rc6Nb+X+zdrNz/f5WKfywvZOd4xctil3jrsSzq/+GSUJRjWVrH7dIrOoVxKwi1aNFCK1euVPv27fNcvmLFCrVo0cKdXRZZ9erV5e/vn2smJyUlReHh4XluEx4e7tb6khQUFKSgoKBc4wEBAbkOYl5j5Y0NPUp29Jlfjzc1rqWYFpH6fPvRXD8Ye7aMUOcbapVZjbWrBejv0U31wmXnJt3b4Tp9uP7g/7t32UlE2dKC74+qb8f6irr+9xNjS/NYrtv3mxZuvfQzpeBa+rSrq7mb8r/c/a72dfOsc/SfbtSynb8q47Lzjir6+WtUzxYKCLj42qUN/18l9/r89qfjGjZro6YN6uAVJ0pL3nssC66rdGrJr8/SPG5F7cWtCPaXv/xFEydO1NKlS3MtW7JkiV588UX95S9/cWeXRRYYGKj27dtr1apVzrGcnBytWrXK5aWyy0VFRbmsL0nx8fH5rg/Yypve1uHKiwnOZmV7zTuyu/Pu8MV93zCuLHWfN7wHVl689Vh6S13ectzcCkIPP/yw+vTpozvvvFPNmzfXXXfdpbvuukvNmjVTnz591KtXLz388MOlVatGjBih//u//9PMmTO1c+dOPfroozpz5oyGDh0q6eIbPl5+MvUTTzyhZcuW6d///rd27dqlcePGaePGjaVyMjfgy7zlB6OU+8q2e9vX8Zp3ZHf33eGLGzC5stQ93vAeWPnx1mPpDXV5y3Fz+0W5Dz/8UHPnzlXjxo31448/avfu3WrSpInmzJmjOXPmlEaNTv369dOkSZM0ZswYtWnTRklJSVq2bJlq1bo4dX/w4EElJyc71+/cubNmz56t9957T61bt9ann36qhQsX6sYbc78uD9jOG34wXnL5e8F40zuyu1tLcQOmt70xoDfzhvfAKoi3HktP1+VNx82tc4Sys7M1adIkLV68WJmZmfrTn/6kcePGqWLFiqVVXy6PP/54vjM6CQkJucbuvfde3XvvvaVcFeD7Lv1gHDZro1f8wL785Ml//qm54q84udNTL925W8vgzvU1e8NB/fTrGbcC5qUw6E0n/3qjgt4D663+bT1UlStvPZaerMubjptb3b/00kt67rnnVKlSJdWuXVtvvfWWHnvssdKqDUAZ86Z35b2cN710524tV/OXt7f94vQ2vvTmgN56LD1Rl7cdN7eegVmzZumdd97R8uXLtXDhQi1ZskQfffSRcnK848Q0AFfPW39ge9NLd+7W4q0B09e5c/I6vIe3HTe3fuIdPHhQd9xxh/N+dHS0HA6Hjhwp+BORAeBqefqchqutxVsDpi9z9+R1eAdvO25ufWdeuHBBwcGu078BAQE+/TboAHyHN82seFMttvKmE+lRdN523Nw6WdoYoyFDhri84eD58+f1yCOP6JprrnGOzZ8/v+QqBIDLeNPMijfVYitvOpEeRedNx82t7+LBgwerZs2aqlKlivN2//33KzIy0mUMAICy4E0n0qPovOm4uTUjNGPGjNKqAwCAYinuWxTAs7zluDGvC5SxC17y9v9AeeFNJ9Kj6LzluPG/BShD3/50XG0nxmv9T97z/iZAecDJ677JG44bQQgoI97yAYNAecXJ677J08eN/zVAGfGWDxgEAPyOIASUAW/6gEEAwO8IQkAZKOgDBgEAnkMQAkqZt33AIADgdwQhoJR52wcMAgB+RxACSpm3fcAgAOB3BCGglHnbBwwCAH5HEALKwD//1FwB/q5BiA+GBADPIwgBZcCbPmAQAPA7ghBQRgZ3rq+GNa6RJD4YEgC8BEEIKCPe8gGDAIDfVfB0AYBNLn3AoKc/WwcAcBE/jYEyRggCAO/BT2QAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1fCYInThxQgMHDlRoaKjCwsL04IMP6vTp0wVu07VrVzkcDpfbI488UkYVAwAAb1fB0wUU1cCBA5WcnKz4+HhlZWVp6NChevjhhzV79uwCtxs2bJgmTJjgvB8SElLapQIAAB/hE0Fo586dWrZsmb777jt16NBBkvSf//xHd9xxhyZNmqTIyMh8tw0JCVF4eHhZlQoAAHyITwShxMREhYWFOUOQJEVHR8vPz0/r16/XXXfdle+2H330kT788EOFh4erV69eev755wucFcrIyFBGRobzfnp6uiQpKytLWVlZzq8v/7c8sqFHyY4+behRsqNPG3qU7OjThh4lz/ZZ1Md0GGNMKddy1V566SXNnDlTu3fvdhmvWbOmxo8fr0cffTTP7d577z3Vq1dPkZGR2rp1q5599ll17NhR8+fPz/exxo0bp/Hjx+canz17Ni+rAQDgI86ePasBAwYoLS1NoaGh+a7n0RmhUaNG6ZVXXilwnZ07dxZ7/w8//LDz65YtWyoiIkK333679u3bp+uvvz7PbUaPHq0RI0Y476enp6tOnTqKiYlxPpFZWVmKj49Xt27dFBAQUOz6vJkNPUp29GlDj5IdfdrQo2RHnzb0KHm2z0uv6BTGo0Fo5MiRGjJkSIHrNGzYUOHh4Tp27JjL+IULF3TixAm3zv/p1KmTJGnv3r35BqGgoCAFBQXlGg8ICMh1EPMaK29s6FGyo08bepTs6NOGHiU7+rShR8kzfRb18TwahGrUqKEaNWoUul5UVJRSU1O1adMmtW/fXpL05ZdfKicnxxluiiIpKUmSFBERUax6AQBA+eIT7yPUrFkzde/eXcOGDdOGDRv0zTff6PHHH9d9993nvGLs8OHDatq0qTZs2CBJ2rdvnyZOnKhNmzbpwIEDWrx4sQYNGqRbb71VrVq18mQ7AADAS/hEEJIuXv3VtGlT3X777brjjjt0880367333nMuz8rK0u7du3X27FlJUmBgoFauXKmYmBg1bdpUI0eO1N13360lS5Z4qgUAAOBlfOLyeUmqVq1agW+eWL9+fV1+AVydOnW0evXqsigNAAD4KJ+ZEQIAAChpBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABr+UwQevHFF9W5c2eFhIQoLCysSNsYYzRmzBhFRESoYsWKio6O1p49e0q3UAAA4DN8JghlZmbq3nvv1aOPPlrkbV599VW99dZbmjJlitavX69rrrlGsbGxOn/+fClWCgAAfEUFTxdQVOPHj5ckxcXFFWl9Y4zeeOMN/fOf/1Tv3r0lSbNmzVKtWrW0cOFC3XfffaVVKgAA8BE+E4TctX//fh09elTR0dHOsSpVqqhTp05KTEzMNwhlZGQoIyPDeT89PV2SlJWVpaysLOfXl/9bHtnQo2RHnzb0KNnRpw09Snb0aUOPkmf7LOpjOowxppRrKVFxcXEaPny4UlNTC1xv3bp1uummm3TkyBFFREQ4x/v27SuHw6G5c+fmud24ceOcs0+Xmz17tkJCQq6qdgAAUDbOnj2rAQMGKC0tTaGhofmu59EZoVGjRumVV14pcJ2dO3eqadOmZVSRNHr0aI0YMcJ5Pz09XXXq1FFMTIzziczKylJ8fLy6deumgICAMqutLNnQo2RHnzb0KNnRpw09Snb0aUOPkmf7vPSKTmE8GoRGjhypIUOGFLhOw4YNi7Xv8PBwSVJKSorLjFBKSoratGmT73ZBQUEKCgrKNR4QEJDrIOY1Vt7Y0KNkR5829CjZ0acNPUp29GlDj5Jn+izq43k0CNWoUUM1atQolX03aNBA4eHhWrVqlTP4pKena/369W5deQYAAMovn7l8/uDBg0pKStLBgweVnZ2tpKQkJSUl6fTp0851mjZtqgULFkiSHA6Hhg8frhdeeEGLFy/Wtm3bNGjQIEVGRqpPnz4e6gIAAHgTn7lqbMyYMZo5c6bzftu2bSVJX331lbp27SpJ2r17t9LS0pzrPPPMMzpz5owefvhhpaam6uabb9ayZcsUHBxcprUDAADv5DNBKC4urtD3ELryAjiHw6EJEyZowoQJpVgZAADwVT7z0hgAAEBJIwgBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACsRRACAADWIggBAABrEYQAAIC1CEIAAMBaBCEAAGAtghAAALAWQQgAAFiLIAQAAKxFEAIAANYiCAEAAGsRhAAAgLUIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYy2eC0IsvvqjOnTsrJCREYWFhRdpmyJAhcjgcLrfu3buXbqEAAMBnVPB0AUWVmZmpe++9V1FRUXr//feLvF337t01Y8YM5/2goKDSKA8AAPggnwlC48ePlyTFxcW5tV1QUJDCw8OLvH5GRoYyMjKc99PT0yVJWVlZysrKcn59+b/lkQ09Snb0aUOPkh192tCjZEefNvQoebbPoj6mwxhjSrmWEhUXF6fhw4crNTW10HWHDBmihQsXKjAwUFWrVtUf//hHvfDCC7r22mvz3WbcuHHO0HW52bNnKyQk5GpKBwAAZeTs2bMaMGCA0tLSFBoamu965ToIffzxxwoJCVGDBg20b98+Pffcc6pUqZISExPl7++f5zZ5zQjVqVNHv/32m/OJzMrKUnx8vLp166aAgIAS6cvb2NCjZEefNvQo2dGnDT1KdvRpQ4+SZ/tMT09X9erVCw1CHn1pbNSoUXrllVcKXGfnzp1q2rRpsfZ/3333Ob9u2bKlWrVqpeuvv14JCQm6/fbb89wmKCgoz/OIAgICch3EvMbKGxt6lOzo04YeJTv6tKFHyY4+behR8kyfRX08jwahkSNHasiQIQWu07BhwxJ7vIYNG6p69erau3dvvkEIAADYw6NBqEaNGqpRo0aZPd6hQ4d0/PhxRURElNljAgAA7+Uz7yN08OBBJSUl6eDBg8rOzlZSUpKSkpJ0+vRp5zpNmzbVggULJEmnT5/W008/rW+//VYHDhzQqlWr1Lt3bzVq1EixsbGeagMAAHgRn7l8fsyYMZo5c6bzftu2bSVJX331lbp27SpJ2r17t9LS0iRJ/v7+2rp1q2bOnKnU1FRFRkYqJiZGEydO5L2EAACAJB8KQnFxcYW+h9DlF8BVrFhRy5cvL+WqAACAL/OZl8YAAABKGkEIAABYy2deGvOUSy+3XfqoDeniG0SdPXtW6enp5fb9H2zoUbKjTxt6lOzo04YeJTv6tKFHybN9Xvq9Xdj7RhOECnHq1ClJUp06dTxcCQAAcNepU6dUpUqVfJf73EdslLWcnBwdOXJElStXlsPhkPT7x2788ssvBb5tty+zoUfJjj5t6FGyo08bepTs6NOGHiXP9mmM0alTpxQZGSk/v/zPBGJGqBB+fn667rrr8lwWGhparv8DS3b0KNnRpw09Snb0aUOPkh192tCj5Lk+C5oJuoSTpQEAgLUIQgAAwFoEoWIICgrS2LFjy/U7VNvQo2RHnzb0KNnRpw09Snb0aUOPkm/0ycnSAADAWswIAQAAaxGEAACAtQhCAADAWgQhAABgLYJQIQ4cOKAHH3xQDRo0UMWKFXX99ddr7NixyszMLHC78+fP67HHHtO1116rSpUq6e6771ZKSkoZVV08L774ojp37qyQkBCFhYUVaZshQ4bI4XC43Lp37166hV6F4vRojNGYMWMUERGhihUrKjo6Wnv27CndQq/SiRMnNHDgQIWGhiosLEwPPvigTp8+XeA2Xbt2zXUsH3nkkTKquGjefvtt1a9fX8HBwerUqZM2bNhQ4Prz5s1T06ZNFRwcrJYtW+rzzz8vo0qLz50e4+Lich2z4ODgMqzWfWvWrFGvXr0UGRkph8OhhQsXFrpNQkKC2rVrp6CgIDVq1EhxcXGlXufVcrfPhISEXMfS4XDo6NGjZVNwMfzrX//S//zP/6hy5cqqWbOm+vTpo927dxe6nbd9XxKECrFr1y7l5ORo6tSp2rFjhyZPnqwpU6boueeeK3C7J598UkuWLNG8efO0evVqHTlyRH/+85/LqOriyczM1L333qtHH33Ure26d++u5ORk523OnDmlVOHVK06Pr776qt566y1NmTJF69ev1zXXXKPY2FidP3++FCu9OgMHDtSOHTsUHx+vpUuXas2aNXr44YcL3W7YsGEux/LVV18tg2qLZu7cuRoxYoTGjh2rzZs3q3Xr1oqNjdWxY8fyXH/dunXq37+/HnzwQW3ZskV9+vRRnz59tH379jKuvOjc7VG6+I69lx+zn3/+uQwrdt+ZM2fUunVrvf3220Vaf//+/erZs6duu+02JSUlafjw4XrooYe0fPnyUq706rjb5yW7d+92OZ41a9YspQqv3urVq/XYY4/p22+/VXx8vLKyshQTE6MzZ87ku41Xfl8auO3VV181DRo0yHd5amqqCQgIMPPmzXOO7dy500gyiYmJZVHiVZkxY4apUqVKkdYdPHiw6d27d6nWUxqK2mNOTo4JDw83r732mnMsNTXVBAUFmTlz5pRihcX3ww8/GEnmu+++c4598cUXxuFwmMOHD+e7XZcuXcwTTzxRBhUWT8eOHc1jjz3mvJ+dnW0iIyPNv/71rzzX79u3r+nZs6fLWKdOncxf//rXUq3zarjbozvfq95IklmwYEGB6zzzzDOmRYsWLmP9+vUzsbGxpVhZySpKn1999ZWRZE6ePFkmNZWGY8eOGUlm9erV+a7jjd+XzAgVQ1pamqpVq5bv8k2bNikrK0vR0dHOsaZNm6pu3bpKTEwsixLLVEJCgmrWrKkmTZro0Ucf1fHjxz1dUonZv3+/jh496nIsq1Spok6dOnntsUxMTFRYWJg6dOjgHIuOjpafn5/Wr19f4LYfffSRqlevrhtvvFGjR4/W2bNnS7vcIsnMzNSmTZtcjoOfn5+io6PzPQ6JiYku60tSbGys1x634vQoSadPn1a9evVUp04d9e7dWzt27CiLcsuMrx3Hq9WmTRtFRESoW7du+uabbzxdjlvS0tIkqcDfj954PPnQVTft3btX//nPfzRp0qR81zl69KgCAwNznYNSq1Ytr369tzi6d++uP//5z2rQoIH27dun5557Tj169FBiYqL8/f09Xd5Vu3S8atWq5TLuzcfy6NGjuabTK1SooGrVqhVY84ABA1SvXj1FRkZq69atevbZZ7V7927Nnz+/tEsu1G+//abs7Ow8j8OuXbvy3Obo0aM+ddyK02OTJk00ffp0tWrVSmlpaZo0aZI6d+6sHTt25Pth0b4mv+OYnp6uc+fOqWLFih6qrGRFRERoypQp6tChgzIyMjRt2jR17dpV69evV7t27TxdXqFycnI0fPhw3XTTTbrxxhvzXc8bvy+tnREaNWpUniemXX678ofP4cOH1b17d917770aNmyYhyp3T3H6dMd9992nO++8Uy1btlSfPn20dOlSfffdd0pISCi5JgpR2j16i9Lu8+GHH1ZsbKxatmypgQMHatasWVqwYIH27dtXgl2gJEVFRWnQoEFq06aNunTpovnz56tGjRqaOnWqp0uDm5o0aaK//vWvat++vTp37qzp06erc+fOmjx5sqdLK5LHHntM27dv18cff+zpUtxm7YzQyJEjNWTIkALXadiwofPrI0eO6LbbblPnzp313nvvFbhdeHi4MjMzlZqa6jIrlJKSovDw8Ksp223u9nm1GjZsqOrVq2vv3r26/fbbS2y/BSnNHi8dr5SUFEVERDjHU1JS1KZNm2Lts7iK2md4eHiuk2svXLigEydOuPX/r1OnTpIuzoJef/31btdbkqpXry5/f/9cV14W9D0VHh7u1vqeVpwerxQQEKC2bdtq7969pVGiR+R3HENDQ8vNbFB+OnbsqLVr13q6jEI9/vjjzosyCpuJ9MbvS2uDUI0aNVSjRo0irXv48GHddtttat++vWbMmCE/v4In0tq3b6+AgACtWrVKd999t6SLVwIcPHhQUVFRV127O9zpsyQcOnRIx48fdwkNpa00e2zQoIHCw8O1atUqZ/BJT0/X+vXr3b667moVtc+oqCilpqZq06ZNat++vSTpyy+/VE5OjjPcFEVSUpIklemxzE9gYKDat2+vVatWqU+fPpIuTsWvWrVKjz/+eJ7bREVFadWqVRo+fLhzLD4+vsy/B4uqOD1eKTs7W9u2bdMdd9xRipWWraioqFyXV3vzcSxJSUlJXvH9lx9jjP7+979rwYIFSkhIUIMGDQrdxiu/Lz12mraPOHTokGnUqJG5/fbbzaFDh0xycrLzdvk6TZo0MevXr3eOPfLII6Zu3brmyy+/NBs3bjRRUVEmKirKEy0U2c8//2y2bNlixo8fbypVqmS2bNlitmzZYk6dOuVcp0mTJmb+/PnGGGNOnTplnnrqKZOYmGj2799vVq5cadq1a2duuOEGc/78eU+1USB3ezTGmJdfftmEhYWZRYsWma1bt5revXubBg0amHPnznmihSLp3r27adu2rVm/fr1Zu3atueGGG0z//v2dy6/8P7t3714zYcIEs3HjRrN//36zaNEi07BhQ3Prrbd6qoVcPv74YxMUFGTi4uLMDz/8YB5++GETFhZmjh49aowx5oEHHjCjRo1yrv/NN9+YChUqmEmTJpmdO3easWPHmoCAALNt2zZPtVAod3scP368Wb58udm3b5/ZtGmTue+++0xwcLDZsWOHp1oo1KlTp5zfd5LM66+/brZs2WJ+/vlnY4wxo0aNMg888IBz/Z9++smEhISYp59+2uzcudO8/fbbxt/f3yxbtsxTLRSJu31OnjzZLFy40OzZs8ds27bNPPHEE8bPz8+sXLnSUy0U6tFHHzVVqlQxCQkJLr8bz54961zHF74vCUKFmDFjhpGU5+2S/fv3G0nmq6++co6dO3fO/O1vfzNVq1Y1ISEh5q677nIJT95o8ODBefZ5eV+SzIwZM4wxxpw9e9bExMSYGjVqmICAAFOvXj0zbNgw5w9tb+Ruj8ZcvIT++eefN7Vq1TJBQUHm9ttvN7t37y774t1w/Phx079/f1OpUiUTGhpqhg4d6hL2rvw/e/DgQXPrrbeaatWqmaCgINOoUSPz9NNPm7S0NA91kLf//Oc/pm7duiYwMNB07NjRfPvtt85lXbp0MYMHD3ZZ/5NPPjGNGzc2gYGBpkWLFuazzz4r44rd506Pw4cPd65bq1Ytc8cdd5jNmzd7oOqiu3SZ+JW3S30NHjzYdOnSJdc2bdq0MYGBgaZhw4Yu35/eyt0+X3nlFXP99deb4OBgU61aNdO1a1fz5Zdfeqb4Isrvd+Plx8cXvi8dxhhTmjNOAAAA3sraq8YAAAAIQgAAwFoEIQAAYC2CEAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAMqVIUOGyOFwyOFwKDAwUI0aNdKECRN04cIFSRc/KPK9995Tp06dVKlSJYWFhalDhw564403dPbsWUnSjh07dPfdd6t+/fpyOBx64403PNgRgNJEEAJQ7nTv3l3Jycnas2ePRo4cqXHjxum1116TJD3wwAMaPny4evfura+++kpJSUl6/vnntWjRIq1YsUKSdPbsWTVs2FAvv/yywsPDPdkKgFLGZ40BKFeGDBmi1NRULVy40DkWExOjU6dO6cknn1S/fv20cOFC9e7d22U7Y4zS09NVpUoVl/H69etr+PDhGj58eBlUD6CsMSMEoNyrWLGiMjMz9dFHH6lJkya5QpAkORyOXCEIQPlHEAJQbhljtHLlSi1fvlx//OMftWfPHjVp0sTTZQHwIgQhAOXO0qVLValSJQUHB6tHjx7q16+fxo0bJ84EAHClCp4uAABK2m233aZ3331XgYGBioyMVIUKF3/UNW7cWLt27fJwdQC8CTNCAMqda665Ro0aNVLdunWdIUiSBgwYoB9//FGLFi3KtY0xRmlpaWVZJgAvQBACYI2+ffuqX79+6t+/v1566SVt3LhRP//8s5YuXaro6Gh99dVXkqTMzEwlJSUpKSlJmZmZOnz4sJKSkrR3714PdwCgpHH5PIByJa/L5y+Xk5Oj9957T9OnT9eOHTtUoUIF3XDDDRo0aJCGDRumihUr6sCBA2rQoEGubbt06aKEhITSbQBAmSIIAQAAa/HSGAAAsBZBCAAAWIsgBAAArEUQAgAA1iIIAQAAaxGEAACAtQhCAADAWgQhAABgLYIQAACwFkEIAABYiyAEAACs9f8Dt0qiZJBvg70AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot y uisng both eigenvectors\n",
    "plt.scatter(y[0,:],y[1,:], marker='d')\n",
    "plt.suptitle(\"PCA Data\", fontsize=12, fontweight='bold')\n",
    "plt.title(\"(THA076BEI005 & THA076BEI025)\", fontsize=10)\n",
    "plt.xlabel(\"PC1\")\n",
    "plt.ylabel(\"PC2\")\n",
    "plt.axis('equal')\n",
    "plt.grid('True')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9098fa9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot y uisng one eigenvector\n",
    "y_1d = np.dot(eigenvector.T[:,0],mat_product.T)\n",
    "\n",
    "plt.scatter(y_1d, np.zeros_like(y_1d), marker='d')\n",
    "plt.suptitle(\"PCA Data (1D)\", fontsize=12, fontweight='bold')\n",
    "plt.title(\"(THA076BEI005 & THA076BEI025)\", fontsize=10)\n",
    "plt.xlabel(\"PC1\")\n",
    "plt.axis('equal')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}